Variable speed of light (VSL) theory. Will The James
Webb telescope falsify Big Bang and Dark Energy?
Otto Krog and Henrik Bohr, The Technical University of Denmark, Lyngby, Denmark.
The purpose of this paper is to show what consequences might come out of a variable speed of light
(VSL), especially in the case of much larger light velocity in the past. In that case the universe is
much larger much older than hitherto imagined.
It is expected that the James Webb telescope in 2019 will observe galaxies close to the event of the
cosmic microwave background (CMB) radiation (the socalled last scattering). Such an observation
together with VSL, could lead to arguments for much more matter in the universe, explaining the
problem of dark energy and falsify Big Bang.
There have been many attempts to create cosmological models based on the assumption that the
velocity of light was much larger in the beginning of the universe evolution just after the so-called
Big Bang. This assumption of VLS (Variable Speed of Light) will solve many problems in
cosmology and change the standard model of the observable universe. Most noticeably the dark
energy cosmology can be done away with and similarly the area of inflationary expansion.
Historically, the first suggestion of VSL was proposed by Einstein, (ref.1.), who first mentioned a
variable light velocity in 1907. Later in 1911 he considered the role of gravity where light can be
slowed down in a gravitational field like the fact that clocks will run slower in a strong gravitational
field and similarly the corresponding frequency, ν, is changed by ν1 = ν2(1 + GM/r c2).
The fact that the light velocity is slowed down by passage through a medium, such as glass where it
is changed 50%, is used as an argument for the slowing (forward in time) of light in the early
universe. Consensus in cosmology considers the early stages after the Big Bang, as having most of
the energy in the form of radiation which had a dominated role in the expansion of the early
universe. The later stages is then considered to be dominated by matter. The role of mass versus
radiation was crucial for the future stages of the universe evolution.
We believe that light velocity was much higher in the early universe than later, when the medium or
energy density slowed the light as is done, for example in the medium of water and of glass.
Dicke developed a theory of VSL where both the frequency and the wavelength in the equation c =
ν λ vary in time and results in a larger change of the light speed c. In explaining the bending of light
by the gravity of the sun, Dicke assumed that the refractive index n should depend on the gravity
parameters as, n = c/c0 = 1 + 2GM/rc2, where c0 is the speed of light far from all masses, M is the
solar mass and G is the gravity constant. Since the total mass in the universe strongly increases in
the mass dominated period of the evolution of the Universe, the speed of light will decrease. In the
right hand side of the equation the left term 1 is relative large and Dicke considered it to be due to
the remainding mass in the universe. The main term, 2GM/rc2 is depending on the mass of the sun
As mentioned above, many theoretical physicists are debating VSL and other natural constants.
(ref.1-3) (Einstein, Dicke). Also others have been studying VSL (Will, Unzicker, Petit, Moffat) (ref.
4-7) in different frameworks or with different arguments. Recently, as described in the science
literature, (ref. 8), Magueijo and Afshordi have proposed a cosmological model where the light
velocity basically was infinite at the birth of the universe where temperatures were trillions of
celcius and which could be detected in the microwave background when more accuracy was
obtained in the observations. Such a possibility for VSL also makes the assumption of an
inflationary era superfluous.
In classical physics, it was generally accepted that light appeared instantaneously at different places.
However, several hundred years ago, scientists (ref. 9) (Rømer) were able to determine a finite
velocity of light from astronomical observations.
As mentioned above, in the beginning of the century Albert Einstein suggested VSL on the reason
of time dilation in relativity (ref. 1, 2) and its relation to redshift, and Dicke did the same in 1957,
(ref. 3). John Moffat, argues for a c that is 30 orders of magnitude smaller today, than in Big Bang.
This article describes how dark energy might be explained by VSL, and the article predicts, that
observations from The James Webb telescope will show huge galaxies very close to “the last
scattering”, (app. 370.000 years after Big Bang, according to cosmology.).
If these galaxies are observed as predicted, the Big Bang Theory will have to be discarded, as it
takes more than a billion year to create huge galaxies and clusters of galaxies.
Another conclusion is, that what we see as the Cosmic microwave background (ref. 10) is just the
border of the observable universe. The universe continues behind that border, being much bigger
than we ever imagined.
Therefore we hypothezise:
The speed of light close to the last scattering is considerably higher, than the one we measure in the
solar system. This will be tested by the James Webb telescope (ref. 11) in 2019, by observing
galaxies so close to the last scattering, that they by no means could have been formed in this short
time-span, according to the usual Big Bang Theory.
The effect of the change in speed of light could be an explanation of dark energy, and actually a
Hubble constant close to zero. Furthermore, the redshift we observe from distant galaxies is a
consequence of a much larger speed of light in the past.
In the following we will give numerical facts in support of this scenario.
The purpose of this analysis is to show how cosmological redshift could be interpreted as a variable
speed of light, instead of the usual interpretation, expanding space. Furthermore it describes a new
understanding of our Universe. If the James Webb Telescope observes full grown galaxies very
close to the CMB (Cosmic Microwave Background) (ref. 10), the Big Bang theory doesn't allow
time enough for the creation of those galaxies.
The redshift factor in cosmology, z, is determined by
From the above we get:
λobs = (1 + z)λemit
It is our assumption that the observed wavelength is directly proportional to the speed of light c in
“vacuum” at present time.
In present time z is zero and the speed of light is what we know as c.
When z is 1 the speed of light is 2c, when z is 2 the speed of light is 3c etc.
Hence we have a cvsl (variable speed of light) described by
cvsl = (1+z)c
The further back in time the higher redshift factor z, and the higher speed of light.
In the figure below, redshift z from 0 to 20 is compared to the age of the universe, as we calculate it
from today as year zero. Modern cosmology interprets this redshift as expanding space.
Calculations of z is done by cosmological calculator from Fermilab. (ref. 12.)
The following figure shows how redshift z behaves within the last billion years. Notice that it
practically is a straight line. Up untill the nineties, this was interpreted as an expanding universe. In
the nineties observations began to show an exponentially rising redshift which was interpreted as an
accellerating expanding universe. Z has to be above 5 to really make an exponential rise.
Lets take the redshift observed one billion years ago where the line still is very straight.
Redshift z is observed to be 0.0735 one billion years ago. (ref. 12.)
That gives us a variable speed of light:
cvsl = (1+z)c = (1+0.0735)c = 1.0735c
If the speed of light varies in one billion years, then the distance varies too.
What was supposed to be one billion lightyears away is not precise one billion years ago in this
VSL theory. If the speed of light decellerated during that period, the age will be slightly different.
Thus we have to find the exact age of the universe at a redshift of 0.0735 in this VSL theory.
The formula is:
t = 2s/(v+v0 )
where s is distance and v0 is velocity one billion years ago and v is the speed of light at present.
If the distance is one billion lightyears, then we think that the time it takes to travel is one billion
years. If the speed of light one billion year ago was higher, and decellerated to our known speed, the
time to travel one billion light years doesn't take one billion years.
t = 2*1 billion lightyears / (1 + 1.0735)c = 0.9646 billion years, when z = 0.0735.
One billion years ago in normal cosmology is thus only 0.9646 billion years ago in this VSL theory.
z one billion years ago in this VSL theory hence is 0.0735/0.9646 = 0.0762
Therefore we get:
VSL one billion years ago:
cvsl = (1 + 0.0762)c = 1.0762c
For every one billion year, VSL increases by 0.0762c
This direct proportion is easily put into a function that shows how VSL evolves in age:
cvsl(x) = (1 + 0.0762x)c
As can be seen from the next diagram, we get a complete different age of the universe through
space and time.
The above function can be written as
x = (cvsl(x) – 1c) / 0.0762c
where x is time in billion years
Our earliest galaxy observation of redshift is at z = 11. That is equivalent to VSL = 12c.
When z is 11 and VSL is 12c we get this result:
x = (cvsl(x) – 1c)/0.0762c = (12c – 1c)/0.0762c =
144.36 billion years, compared to the age in normal cosmology of a z at 11 which
gives an age of 13.36 billion years.
The higher redshift the more distant and back in time we observe, and the higher the speed of light.
Possible experimental observations and the James Webb
Our prediction is that it will show galaxies much closer to the CMB, than observed before. These
galaxies will be so developed and old, that they cannot have grown that big in the short time the Big
Bang theory allows.
The earliest galaxy we have observed has the name GN-Z11. The light observed from that galaxy is
about 13.4 billion years old. The galaxy is observed 400 million years after the Big Bang.
According to current theory, it can only be a protogalaxy as it takes almost 2 billion years to create a
galaxy the size of, for instance, the Milky Way.
James Webb will be able to observe much closer to the CMB, and with much better resolution, than
telescopes has done before. Therefore, it is our prediction that James Webb will show full grown
galaxies much closer to the CMB than usual theories allow.
Furthermore we postulate that what we know as the CMB is a veil of electromagnetism, which we
can not see through. The radiation should not be understood as the afterglow of the Big Bang, but as
a boundary to a universe much larger and much older behind.
The recent discovery of the quasar 690 million years after Big Bang is the latest discovery of
astronomical observation that poses a problem in the usual Big Bang Theory. (ref. 14.)
The known universe as we observe it, is perhaps a small village, compared to the universe we
cannot yet observe. The fluctuations of heat in the CMB might indicate different clusters of galaxies
in the universe behind this veil.
Prediction and consequences:
The James Webb telescope will show huge fullgrown galaxies in a redshift area very close to CMB.
This observation will not align with our mainstream understanding of the Big Bang theory.
If the above is true it has 2 major consequences:
Space is not expanding or accelerating, which falsifies the theory of Dark Energy.
Big galaxies will be observed very close to CMB, which falsifies the Big Bang theory.
Other natural constants:
If c is variable in space and time, it is naive to think, that other natural constants as for example G,
the constant of gravity, isn't variable as well. If all other natural constants is merged into this theory,
it is most likely that VSL is different than described in the function above. Diracs big number theory
suggested changing natural constants. (ref. 15.)
The VSL theory is just a simple explanation of our thoughts. A lot of work has to be done, if James
Webb observes what we suspect it will.
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ref.12. http://home.fnal.gov/~gnedin/cc/ All redshift z's in this paper, are calculated by this
cosmological calculator from Nick Gnedin, Fermilab.
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